- #1
Nusc
- 760
- 2
Homework Statement
Given some dispersion relation for the tight binding approximation in 2D:
e(k_x,k_y) = -2t_1[cos(k_x*a)+cos(k_y*a)]-4t_2[cos(k_x*a)cos(k_y*a)]
Show that the density of states has a logarithmic singularity for some choice of parameters t_i.
Homework Equations
g(e)de=g integral dS/(2*pi)^3 *1/|grad e(K)|
The Attempt at a Solution
When it says logaritmic singularity is it referring to von hove singularity?
First I expanded the cosines.
-2t_1[2-k_x^2*a^2/2 -k_y^2*a^2/2] -4t_2[1+k_x^2*a^2 k_y^2*a^2
Then what do I do?